I want to perform a statistical test: Wilcoxon Signed Rank Test to test if there is a significant difference between them, but I don't know if the two samples are dependent or not? Context: I have a dataset that contains a set of elements, I want to predict the dependent variable, I use two models A and B to perform the prediction using LOOCV. So, I have two samples based on the absolute errors (sample A: contains the absolute errors based on prediction of Model A, Sample B: contains the absolute erroers based on prediction of Model B). My Question: is the sample A and B are dependent or independent? Thank you in advance
The answer is dependent. Or, to be a bit more precise: paired.
The thing to keep in mind here is that you only have one sample, and have two measurements for each observations in that sample.
If, instead, you had two distinct samples (e.g., one representing the first 100 cases in your data set and the other the second 100 cases), and were comparing the predictive accuracy between these two samples, you would then have two independent samples.
Two or more samples are said to be dependent, in short, if one sample is dependent or is influenced by another. Suppose, one wants to study earning difference between men and women. So s/he randomly selects 100 men and 100 women, and records interested variable values. In this case, the samples are independent because a man's earning value cannot be related to that of a woman. Let's again say, one collects data of 100 couples. Here, the samples are dependent in that couples tend to have similarities in aspects like level of education, ambition, ethnicity, etc. If one finds factors that are likely to affect samples, then they should be treated as dependent.